1. ## Distance of x

Can anyone help me solve this?

a maan can cycle from his house to a railway station and back in a certain time at 12km/h. if he rides out at 8km/h and returns by motor at 15km/h, he takes 15mins longer on the double journey? Find the distance between his house and the station.

I'm not really sure how to approach this problem. Whether to name the distance x, or use the distance/time formula.

2. Hello bloo.tomarto
Originally Posted by bloo.tomarto
Can anyone help me solve this?

a maan can cycle from his house to a railway station and back in a certain time at 12km/h. if he rides out at 8km/h and returns by motor at 15km/h, he takes 15mins longer on the double journey? Find the distance between his house and the station.

I'm not really sure how to approach this problem. Whether to name the distance x, or use the distance/time formula.

I think you need to do both of the things you've suggested.

Let the distance between his house and the station be $\displaystyle x$ km. Then, using the formula:
$\displaystyle \text{time} = \frac{\text{distance}}{\text{speed}}$
• the time he takes to cycle one way is $\displaystyle \frac{x}{12}$ hours.

• the time he takes to ride one way is $\displaystyle \frac{x}{8}$ hours.

• the time he takes to motor one way is $\displaystyle \frac{x}{15}$ hours.

Finally, the time to ride + time to motor = 2 x time to cycle one way $\displaystyle +\tfrac14$ hour. So we get:
$\displaystyle \frac{x}{8}+\frac{x}{15}= 2\times\frac{x}{12}+\frac14$
Can you complete it now? (Hint: Begin by multiplying both sides by $\displaystyle 120 \;(=8\times15)$ to get rid of fractions.)

(I make the distance between his house and the station $\displaystyle 10$ km.)